The property of the Sun that most affects the strength of its gravitational attraction to Earth is its mass.

Here's why:

* Newton's Law of Universal Gravitation: This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

* Sun's Mass: The Sun is incredibly massive, containing over 99% of the total mass of our solar system. This immense mass is the primary reason why Earth orbits the Sun and experiences its gravitational pull.

While the Sun's other properties like its radius and density also play a role, their impact on gravitational force is significantly smaller compared to its mass.